w/(w-5)-5w/(5w-4)=(w-2)/(5w^2-29w+20)

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Solution for w/(w-5)-5w/(5w-4)=(w-2)/(5w^2-29w+20) equation: 


D( w )

5*w^2-(29*w)+20 = 0

5*w-4 = 0

w-5 = 0

5*w^2-(29*w)+20 = 0

5*w^2-(29*w)+20 = 0

5*w^2-29*w+20 = 0

5*w^2-29*w+20 = 0

DELTA = (-29)^2-(4*5*20)

DELTA = 441

DELTA > 0

w = (441^(1/2)+29)/(2*5) or w = (29-441^(1/2))/(2*5)

w = 5 or w = 4/5

5*w-4 = 0

5*w-4 = 0

5*w-4 = 0 // + 4

5*w = 4 // : 5

w = 4/5

w-5 = 0

w-5 = 0

w-5 = 0 // + 5

w = 5

w in (-oo:4/5) U (4/5:5) U (5:+oo)

w/(w-5)-((5*w)/(5*w-4)) = (w-2)/(5*w^2-(29*w)+20) // - (w-2)/(5*w^2-(29*w)+20)

w/(w-5)-((5*w)/(5*w-4))-((w-2)/(5*w^2-(29*w)+20)) = 0

w/(w-5)-5*w*(5*w-4)^-1-((w-2)/(5*w^2-29*w+20)) = 0

w/(w-5)+(-5*w)/(5*w-4)+(-1*(w-2))/(5*w^2-29*w+20) = 0

5*w^2-29*w+20 = 0

5*w^2-29*w+20 = 0

5*w^2-29*w+20 = 0

DELTA = (-29)^2-(4*5*20)

DELTA = 441

DELTA > 0

w = (441^(1/2)+29)/(2*5) or w = (29-441^(1/2))/(2*5)

w = 5 or w = 4/5

(w-4/5)*(w-5) = 0

w/(w-5)+(-5*w)/(5*w-4)+(-1*(w-2))/((w-4/5)*(w-5)) = 0

(w*(5*w-4)*(w-4/5))/((w-5)*(5*w-4)*(w-4/5))+(-5*w*(w-5)*(w-4/5))/((w-5)*(5*w-4)*(w-4/5))+(-1*(w-2)*(5*w-4))/((w-5)*(5*w-4)*(w-4/5)) = 0

w*(5*w-4)*(w-4/5)-5*w*(w-5)*(w-4/5)-1*(w-2)*(5*w-4) = 0

21*w^2-5*w^2-84/5*w+14*w-8 = 0

16*w^2-14/5*w-8 = 0

16*w^2-14/5*w-8 = 0

2*(8*w^2-7/5*w-4) = 0

8*w^2-7/5*w-4 = 0

DELTA = (-7/5)^2-(-4*4*8)

DELTA = 3249/25

DELTA > 0

w = ((3249/25)^(1/2)+7/5)/(2*8) or w = (7/5-(3249/25)^(1/2))/(2*8)

w = 4/5 or w = -5/8

2*(w+5/8)*(w-4/5) = 0

(2*(w+5/8)*(w-4/5))/((w-5)*(5*w-4)*(w-4/5)) = 0

(2*(w+5/8)*(w-4/5))/((w-5)*(5*w-4)*(w-4/5)) = 0 // * (w-5)*(5*w-4)*(w-4/5)

2*(w+5/8)*(w-4/5) = 0

( w+5/8 )

w+5/8 = 0 // - 5/8

w = -5/8

( w-4/5 )

w-4/5 = 0 // + 4/5

w = 4/5

w in { 4/5} 

w = -5/8

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